R/215_reductions_dgp2dcp_canonicalizers_eye_minus_inv_canon.R

In CVXR: Disciplined Convex Optimization

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## DO NOT EDIT THIS FILE!! EDIT THE SOURCE INSTEAD: rsrc_tree/reductions/dgp2dcp/canonicalizers/eye_minus_inv_canon.R
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## CVXPY SOURCE: reductions/dgp2dcp/canonicalizers/eye_minus_inv_canon.py
## DGP canonicalizer for EyeMinusInv: (I - X)^{-1}
##
## Introduces auxiliary variable U (= log(Y)) where Y >= (I-X)^{-1}.
## Constraint: diag(Y - Y*X) >= 1, canonicalized in log-space as:
##   diag(U + one_minus_pos_canon(YX_canon - U)) >= 0

.dgp_eye_minus_inv_canon <- function(expr, args) {
  X <- args[[1L]]
  n <- expr@args[[1L]]@shape[1L]

  ## U = log(Y), a new free variable in log-space
  U <- Variable(c(n, n))

  ## YX in log-space: matmul(U, X) -- but we need DGP canonicalization
  ## YX = U %*% X (log-space matmul)
  YX <- U %*% X
  YX_canon <- .dgp_mulexpression_canon(YX, YX@args)[[1L]]

  ## one_minus_pos(YX_canon - U): log(1 - exp(YX_canon - U))
  omp_expr <- OneMInusPos(YX_canon - U)
  omp_canon <- .dgp_one_minus_pos_canon(omp_expr, omp_expr@args)[[1L]]

  ## diag(U + omp_canon) >= 0
  lhs_canon <- DiagMat(U + omp_canon)
  list(U, list(lhs_canon >= 0))
}